In the original PTQM proposal [1]} the formula
for \(\Theta _{(Bender)}\) 
was
required to contain a self-adjoint 
operator of charge.
In the alternative
ISP framework of paper [2]}
the same factorization ansatz
admited a
more general charge.
In contrast to its status in PTQM, it was admitted
non-Hermitian  in \({\cal H}_{math}\) . In our
present terminology
the charge \(Z_1\) 
acquired the physical meaning of
another
non-Hermitian and
crypto-Hermitian but
Hermitizable observable-representing operator.
